It is possible to find out using mathematical methods whether a given integer is a prime number or not.
No, 509 809 is not a prime number.
For example, 509 809 can be divided by 47: 509 809 / 47 = 10 847.
For 509 809 to be a prime number, it would have been required that 509 809 has only two divisors, i.e., itself and 1.
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509 809 is an odd number, because it is not evenly divisible by 2.
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A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 509 809 is about 714.009.
Thus, the square root of 509 809 is not an integer, and therefore 509 809 is not a square number.
The square of a number (here 509 809) is the result of the product of this number (509 809) by itself (i.e., 509 809 × 509 809); the square of 509 809 is sometimes called "raising 509 809 to the power 2", or "509 809 squared".
The square of 509 809 is 259 905 216 481 because 509 809 × 509 809 = 509 8092 = 259 905 216 481.
As a consequence, 509 809 is the square root of 259 905 216 481.
The multiples of 509 809 are all integers evenly divisible by 509 809, that is all numbers such that the remainder of the division by 509 809 is zero. There are infinitely many multiples of 509 809. The smallest multiples of 509 809 are: